Antenna length

I have been looking into how antennas work, and I have found that antennas of half wave-length are apparently optimal, but I don't understand why. If anybody could explain why this is, I would appreciate it. Thanks! (I do have an understanding of electromagnetic waves)

an antenna absorbs the electromagnetic radiation most efficiently if it is of the same order of magnitude than the incoming wave. in the same way, if you want to stop an incoming wave on the sea side you are better of with a wall which is as high as the incoming waves rather than tiny bumbs which will be less effective at absorption.

I have been looking into how antennas work, and I have found that antennas of half wave-length are apparently optimal, but I don't understand why. If anybody could explain why this is, I would appreciate it. Thanks! (I do have an understanding of electromagnetic waves)

In simplest terms, the antenna current must be zero at both ends of a half wave antenna, these are called the current nodes. But where the current nodes are zero, the voltage anti-nodes are at maximum. So you have voltage maximums at both ends of the half wave antenna causing the maximum possible antenna current to flow and the maximum amount of electromagnetic radiation from the antenna. For that reason the half wave antenna is considered to be the most efficient.

In general, an antenna should not be shorter than a half wavelength long, but you will find exceptions to this especially at very low frequencies and long wavelengths where even a half wave antenna would be too long to be physically practical. One solution is to use a quarter wave antenna and ground one end, letting the ground act as the other quarter wave, so you still have a half wave antenna. This is known as the Marconi antenna.